Review Reports - Mathematical Knowledge for Teaching the Area of Plane Surfaces: A Literature Review on Professional Noticing

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Summary

This manuscript is a literature review that examines the mathematical knowledge of teachers, specifically in relation to the concept of area of plane surfaces in Basic Education. Grounded in Brazilian educational research and informed by theoretical frameworks such as school mathematics vs. academic mathematics and professional noticing, the article analyzes 18 studies selected through a systematic search of the CAPES Theses and Dissertations Catalog.

General and Specific Comments

Section 1

Although this is a literature review, I could not identify a clear research question, not even implicitly. Please consider articulating what you are aiming to explore, so you can state at least an open research question (for example, this could be added around lines 59–73).

Section 2

It is unclear how Moreira's work is actually integrated into your article. It is mentioned prominently in the abstract, but not referenced at all in Section 5. Is it intended as a paradigmatic premise? I find it highly relevant, but you should clarify its role. The same applies to the concept of professional noticing. Both are addressed in Section 2, which appears to sit halfway between your theoretical framework and your object of analysis. However, these concepts are not revisited in the literature review part (analysis the 18 documents) nor are they indirectly used to define the methodology.

How is Section 2 (noticing and school mathematics in the sense of Moreira) connected to the way you analyzed the selected articles, the criteria under which they were selected and the themes there discussed —such as the more generic mathematical knowledge for teaching, area of plane surfaces, professional learning, etc.? If you do not intend to use a classic model like MKT (Mathematical Knowledge for Teaching), then demonstrate how your perspective can be operationalized, and how you applied it—implying that it might offer advantages (e.g., more flexible or less rigid) compared to existing models like MKT.

Moreover, Section 2 remains very generic. You do not specify what kind of teachers are being discussed. In addition to the elements listed on lines 99–101, it would be helpful to address affective/pedagogical aspects (as referenced in lines 139–143), especially if you are referring to primary education teachers. The teacher should be considered holistically—not only as a professional, but also as an educator in dialogue with their own identity and those of their students.

Sections 2 and 3 appear disconnected. Section 2 does not seem to support Section 3. The brief introduction in lines 180–188 is helpful but should be introduced earlier.

Section 3

At line 227 you mention 17 documents, but from line 248 onward, you refer to 18. Please clarify.
What is the actual time span of the reviewed documents (beyond what is suggested in lines 248–249)? It would also be useful to include a brief overview of the types of documents available in CAPES, since this repository is less familiar to international readers. Are the documents all produced by Brazilian students or researchers?

The reference to Kospentaris at line 330 is unclear. More generally, I find the combination of Brazilian, French, and international sources somewhat difficult to follow (see also my suggestion below regarding the structure of Sections 5.1 and 5.2).

The connection between Tables 1 and 2 and the main text is not fully clear. I recommend either revising the tables or explicitly explaining them within the text.

Section 4

Paragraph 278–285 seems crucial, but it is not clearly articulated. It appears that you are stating how you intend to analyze the selected documents, while also acknowledging that your analytical lens may not align perfectly with the perspectives of those documents. If this is a methodological issue, it should be introduced earlier—either in Section 2 (as a theoretical prelude) or in Section 3 (as part of your methods). The same applies to Section 286–306, which contains important content but appears too late in the paper. About paragraph 278–285 I think clarifying the two aspects — what are you looking and how are you looking at it — can help also further, in section 5.1.

Lines 262 onward: avoid using quotation marks and do not include “(author’s summary)” unless you are directly quoting. Otherwise, it causes confusion.

Lines 346–354 become difficult to follow. It is hard to distinguish between primary and secondary references—i.e., the works you are reviewing and the works cited by those works.

Section 5

Given the relatively small number of documents reviewed, it might be useful to add a summary table in Section 5 to help readers navigate Sections 5.1 and 5.2. You could put (authors’ names, year) into a table. Since it is difficult to distinguish which documents are part of your analytical corpus (object of research), which are part of your theoretical framework, and which are merely cited by the corpus or cited additionally by you, a table could help. Consider using a typographical cue to mark the documents under review—at least on their first mention.

Please verify whether it is acceptable to cite personal communications (p. 11 and elsewhere).

Line 442: please correct “area”.

Figure 1 contains overlapping line numbers and needs to be revised. Maybe the PDF version is different from the docx/odt one.

In Section 5.1, I struggled to distinguish between content derived from the reviewed documents and content from external sources cited within them. At times, the review seems to turn into an exposition of the Game with Frames framework. In my view, Sections 5.1 and 5.2 both require restructuring. While each part is well-written on its own, the content appears in unexpected places, disrupting the logical flow. For instance, in section 5.1, you could begin with a general overview of the Game with Frames framework and then delve into how each author uses it, offering both a clearer panorama of Game with Frames and more analytical engagement with each of your primary sources from CAPES (i.e., what is used of Game with Frames? How is it used? And so on). In section 5.2 I expected a stronger reference to the sources of section 2.

Section 6

The practical implications mentioned in the conclusion are not clearly explained. Where are they drawn from? Link them with section 5.2, and stress them in that section.

Author Response

Dear Revisor,

I greet you and present a revised version of the manuscript originally submitted.

I would like to thank the reviewers for their careful reading and the relevant comments they made about the manuscript.

We have attempted to consider them in this revised version that we are now submitting.

Therefore, seeking to address the comments made by the reviewers:

We have inserted a question into the text and sought to clarify its purpose;
We have included information about the type of studies that comprise the Catalog of Theses and Dissertations;
We have included information about the participants in the studies that comprise the corpus analyzed (teachers and prospective teachers);
We have replaced the initial tables with a table that identifies each study and its purpose;
We sought to improve the theoretical framework, including the meaning of area of 2D shapes in Basic Education in Brazil and develop the meaning of school mathematics and teacher's knowledge.
We asked a professional proofreader to review the English text.
We corrected the typo in the word "area."
Figure 1 was saved in a different format to avoid distortion.

All changes were highlighted in yellow in the revised version.

We hope we have adequately addressed the feedback received.

In any case, we remain available to clarify or improve the text.

Sincerely,

Reviewer 2 Report

Comments and Suggestions for Authors

Review of

Mathematical knowledge of teaching the area of plane surfaces: a literature review on professional teaching.

Aim of the study

“This article aims to identify the mathematical knowledge required for teaching the concept of area of plane surfaces in Basic Education”. (12-13)

“More precisely, it aims to investigate the mathematical knowledge required for teaching the concept of area of plane figures.” (48-49)”

Method of the current study

“Between April and June 2025, a systematic search was conducted in the CAPES Catalog of Theses and Dissertations to identify Brazilian academic literature related to the teaching of mathematical knowledge concerning plane surfaces.” (189-191)

Conclusions of the study in brief (quoted)

“Developing a professional perspective on students’ responses and records related to situations involving the concept of area of plane surfaces requires mathematical knowledge specific to teaching. … For example Lessa noted that they (the teachers) relied on a single technique in the tasks proposed and lacked—even implicitly—“justifications to support the techniques applied.” Essentially, their practice involved “applying formulas without an explicit justification of the reasons that led them to develop such techniques.”

“… we understand that the theoretical frame briefly discussed here has the potential to be recognized within the perspective of school mathematics as mathematical knowledge specific to teaching and, consequently, could contribute to the development of a professional perspective on students’ responses and records.”

“Furthermore, this article opens an interesting window by creating connections between theories and theoretical frames that are not often brought together in research.”

Comments

Comment 1

The aim is very vague and so are the results. There is no real answer to the question of what mathematical knowledge is required for teaching the concept of area of plane figures.

Comment 2

According to my opinion, needs a clear description of the follow points:

Firstly, it needs to add a definition of, or discussion about, theories for mathematical knowledge required for teaching mathematics. In fact, there has been a worldwide debate of this since L. Shulman (1986, 1987) and his division of Mathematical Knowledge for Teaching in Subject Matter Knowledge and Pedagogical Content Knowledge.

Secondly, it needs to add a definition of “concept of area of plane surfaces in Basic Education”. There are in fact many usable theories: Euclidian geometry, van Hiele’s geometry, Projective geometry known from the New Mathematics and based on algebra, etc.

Thirdly, it needs to add a discussion about the teaching-learning process and individual ability to learn.

To sum up, if fundamental concepts in the study are used without clear definitions and description it is difficult to investigate and account for the content of the research material and findings.

Comments on the Quality of English Language

Needs minor revising

Author Response

Dear Revisor,

I greet you and present a revised version of the manuscript originally submitted.

I would like to thank the reviewers for their careful reading and the relevant comments they made about the manuscript.

We have attempted to consider them in this revised version that we are now submitting.

Therefore, seeking to address the comments made by the reviewers:

We have inserted a question into the text and sought to clarify its purpose;
We have included information about the type of studies that comprise the Catalog of Theses and Dissertations;
We have included information about the participants in the studies that comprise the corpus analyzed (teachers and prospective teachers);
We have replaced the initial tables with a table that identifies each study and its purpose;
We sought to improve the theoretical framework, including the meaning of area of 2D shapes in Basic Education in Brazil and develop the meaning of school mathematics and teacher's knowledge.
We asked a professional proofreader to review the English text.
We corrected the typo in the word "area."
Figure 1 was saved in a different format to avoid distortion.

All changes were highlighted in yellow in the revised version.

We hope we have adequately addressed the feedback received.

In any case, we remain available to clarify or improve the text.

Sincerely,

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

After revising

Review of

Mathematical knowledge of teaching the area of plane surfaces: a literature review on professional teaching.

Comment 1

There is still no explanation of the significance of mathematical knowledge of teaching or which types of areas, or techniques for measuring areas that were analyzed in the study. Is it just about polygons or also about ellipses, integrals, Koch´s snowflake etc. This is never clarified and if the reader does not know. Without these parameters, it is not possible to understand the objectivity and outcomes of the study.

Comment 2

Under the headline conclusions, this becomes even more confusing, for examples:

For example, Lessa … noted that the teachers “relied on a single technique in the tasks proposed and lacked - even implicitly - justifications to support the techniques applied.” Essentially, their practice involved “applying formulas without an explicit justification of the reasons that led them to develop such techniques.” (What techniques, applied to what?)

“Findings from … “among others provide evidence that formative actions aimed at expanding the understanding of the concept area … contributed significantly to the teachers participating in the study.” (What formative actions, about what?)

Comment 3

In what way could these statements (the examples above) be used to improve Mathematical knowledge of teaching the area of plane surfaces. There is not one single example of what is going on.

In addition, according to my opinion, the manuscript just contains a lot of conclusions without explanation, analysis and results.

To sum up, if fundamental concepts in the study are used without clear definitions it is difficult to investigate and account for the content of a research material (my sum -comment from the previous review report).

Comments on the Quality of English Language

A more clearly express needs

Author Response

Comment 1

Response 1:

Dear reviewer,

Thank you once again for your careful reading and suggestions.

In our view, the meaning of mathematical knowledge of teaching was already clear in the text. However, we have included a paragraph (lines 190-193) reiterating our understanding of the term.

Regarding the notion of area of flat surfaces, we have included a footnote explaining its meaning in the context of the Brazilian Basic Education curriculum. (footnote 2)

Comment 2

Under the headline conclusions, this becomes even more confusing, for examples:

Response 2:

We have sought to clarify some of the issues raised; however, we believe that it would be beyond the scope of this article to delve into details such as the type of formative actions carried out in the studies, for example. Our focus is on understanding the notion of area of plane surfaces, as expressed in these studies.

We believe that Table 1 provides sufficient context for the research that makes up the corpus of this study.

Comment 3

In what way could these statements (the examples above) be used to improve Mathematical knowledge of teaching the area of plane surfaces. There is not one single example of what is going on.

In addition, according to my opinion, the manuscript just contains a lot of conclusions without explanation, analysis and results.

Response 3:

In our view, the manuscript's structure presents and discusses the results in Section 5. This is done through a presentation and discussion of the predominant theoretical framework in the research that makes up the study's corpus. In the Conclusions, we do not consider it necessary to repeat the ideas already presented.

Observations:

1. Changes made to the text are marked in yellow.

2. We also reiterate that the manuscript was translated by a professional translator. After the second review, we requested that the manuscript be reviewed by a researcher with extensive knowledge of the English language, who found no problems with the writing.

Therefore, it may be worth mentioning the sections where the writing requires attention.